The Neutron Lifetime Anomaly as a Bookkeeping Problem: The Branching Fraction a Dark Channel Must Carry, and What Remains of It

Beam measurements of the free neutron lifetime give 887.7 s and bottle measurements give 877.75 s, a difference of 9.95 s at 4.37 standard deviations. Treating the difference as bookkeeping - a bottle counts survivors (total width) and a beam counts protons (proton-producing partial width) - the required branching fraction into a proton-free (dark) channel is computed to be 1.121 +/- 0.254 percent, with a partial lifetime of 78,309 s. Priced against published constraints, the photon and electron-positron channels are excluded by direct searches, mirror-neutron oscillation in zero mirror field is excluded by a factor of about sixteen in rate, and a non-interacting dark fermion is excluded by neutron-star masses. A fully invisible channel survives only with total final-state mass between 937.993 MeV and 939.565 MeV - a window exactly 1.572 MeV wide - and only with strong repulsive dark self-interactions. All numbers are produced by the deposited Python script.